The discrete-time generalized algebraic Riccati equation: Order reduction and solutions’ structure
MetadataShow full item record
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+Δ of each solution X: The first part is trivial, in the sense that it is an explicit expression of the addend X0 which is common to all solutions, so that it does not depend on the particular X. The second part can be – depending on the structure of the considered generalized Riccati equation – either a reduced-order discrete-time regular algebraic Riccati equation whose associated closed-loop matrix is non-singular, or a symmetric Stein equation. The proposed reduction is explicit, so that it can be easily implemented in a software package that uses only standard linear algebra procedures.
This research was partially supported by the Australian Research Council (grant no. FT120100604)
Showing items related by title, author, creator and subject.
Ferrante, A.; Ntogramatzidis, Lorenzo (2013)This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati ...
On the closed-form solution of the matrix Riccati differential equation for nonsign-controllable pairsNtogramatzidis, Lorenzo; Ferrante, Augusto (2011)In this paper we present explicit closed form formulae for the solution of the matrix Riccati differential equation with a terminal condition. These formulae can still be employed even in the case in which the system is ...
Continuous-time singular linear-quadratic control: Necessary and sufficient conditions for the existence of regular solutionsFerrante, A.; Ntogramatzidis, Lorenzo (2016)The purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear-quadratic (LQ) optimal control. Indeed, in spite of ...